Mathematical Modeling of Physical Processes in Metals and Ordered Alloys

This study presents the results of mathematical modeling of physical processes in metals and ordered alloys using the Lennard-Jones potential and the MATLAB software package. The theoretical part describes the differential equations used for modeling, their initial and boundary conditions, as well as the difference approximation. The molecular dynamics principle has been selected as a modeling technique together with one of the pair potentials. The practical part describes a computational algorithm, as well as a step-by-step development model in the modeling environment. The following results were obtained: The chaotic motion (displacement) of atoms has been studied in two-dimensional and three-dimensional crystal lattices, as well as the distribution of atoms in the modeled cell and outward, the ratio of binding energies in real metals and the computational model has been considered, the interaction potential was determined, which turned out to be positive, and phase–frequency characteristics have been determined, which have passed the stability check.